External data pack error
Because Blender caches textures, they won't appear missing right away, showing pink color. To become pink, they should be reloaded. Like when you reopen the .blend file or append/link their texture data blocks to another .blend file.
Before packing, you have to find all missing textures in the original file.
When you use Find Missing Files, you have to choose the folder with missing files. Blender will search in the folder's subfolders also. To find files on your computer use something like Everything.
In Blender, there is no such concept as a project or a project folder.
There are no requirements for strict directory management like in Unreal Engine.
You may also want to disable using relative paths so you can move a .blend file freely.

Some methods of importing, like with some add-ons, may ignore this setting, so you have to make path absolute manually.